Solution for an arbitrary number of coupled identical oscillators

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Abstract
We propose a solution to the problem of solving the Schrödinger equation for an arbitrary number of identical one-dimensional harmonically coupled oscillators raised by Fan Hong-yi [Phys. Rev. A 42, 4377 (1990)]. The relationship between the Fock spaces associated with the uncoupled and coupled oscillators is given as well as the coordinate representation of the eigenstates. In view of further applications, the Lie algebraic properties of the model are examined, and the generalization to three spatial dimensions is made.